As in the mean-field calculations for the ANNNI model [1]}, given
the temperature and the parameters of the system, the problem consists in
finding a multiple set of numerical solutions, and choosing the solution that
minimizes the free energy. Except in the immediate neighborhood of a critical
line, this search for the physically acceptable solutions becomes a purely
numerical problem. Usually, we find a numerical solution with the assumption
of a periodicity of \(L\)  lattice spacings along the \(z\)  direction, and take
note of the associated value of the free energy. We then repeat this procedure
for a sequence of values of \(L\) . Physically acceptable solutions are shown to
minimize the free energy with respect to the length \(L \) . Instead of carrying
out this cumbersome numerical calculation, we now turn to an expansion of the
free energy.
